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: \( 14.007064483 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.040527347\)
\(a_{6}=+0.408248290\) \(a_{7}=-1.615210152\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.028657162\)
\(a_{11}=-1.795453408\) \(a_{12}=+0.288675135\) \(a_{13}=-0.502960021\) \(a_{14}=-1.142126052\) \(a_{15}=+0.023398474\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.477141328\) \(a_{18}=+0.235702260\) \(a_{19}=+0.571072331\) \(a_{20}=+0.020263673\)
\(a_{21}=-0.932542016\) \(a_{22}=-1.269577280\) \(a_{23}=-0.062464865\) \(a_{24}=+0.204124145\) \(a_{25}=-0.998357534\)
\(a_{26}=-0.355646441\) \(a_{27}=+0.192450090\) \(a_{28}=-0.807605076\) \(a_{29}=-1.764909288\) \(a_{30}=+0.016545220\)
\(a_{31}=-0.052319627\) \(a_{32}=+0.176776695\) \(a_{33}=-1.036605508\) \(a_{34}=+0.337389868\) \(a_{35}=-0.065460181\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.443115471\) \(a_{38}=+0.403809118\) \(a_{39}=-0.290384103\) \(a_{40}=+0.014328581\)
\(a_{41}=-0.495359392\) \(a_{42}=-0.659406783\) \(a_{43}=+0.939358053\) \(a_{44}=-0.897726704\) \(a_{45}=+0.013509116\)
\(a_{46}=-0.044169330\) \(a_{47}=+0.422282629\) \(a_{48}=+0.144337567\) \(a_{49}=+1.608903836\) \(a_{50}=-0.705945382\)
\(a_{51}=+0.275477674\) \(a_{52}=-0.251480010\) \(a_{53}=-1.402436397\) \(a_{54}=+0.136082763\) \(a_{55}=-0.072764962\)
\(a_{56}=-0.571063026\) \(a_{57}=+0.329708764\) \(a_{58}=-1.247979326\) \(a_{59}=+1.549005280\) \(a_{60}=+0.011699237\)
\(a_{61}=+1.751730589\) \(a_{62}=-0.036995563\) \(a_{63}=-0.538403384\) \(a_{64}=+0.125000000\) \(a_{65}=-0.020383635\)
\(a_{66}=-0.732990785\) \(a_{67}=-0.733990038\) \(a_{68}=+0.238570664\) \(a_{69}=-0.036064107\) \(a_{70}=-0.046287338\)
\(a_{71}=+0.577825837\) \(a_{72}=+0.117851129\) \(a_{73}=-1.064444328\) \(a_{74}=-0.313329956\) \(a_{75}=-0.576401988\)
\(a_{76}=+0.285536162\) \(a_{77}=+2.900034576\) \(a_{78}=-0.205332577\) \(a_{79}=-0.999810772\) \(a_{80}=+0.010131829\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.350271985\) \(a_{83}=+0.789197517\) \(a_{84}=-0.466271008\) \(a_{85}=+0.019337272\)
\(a_{86}=+0.664226449\) \(a_{87}=-1.018970852\) \(a_{88}=-0.634788640\) \(a_{89}=-0.575865567\) \(a_{90}=+0.009552387\)
\(a_{91}=+0.812386131\) \(a_{92}=-0.031232433\) \(a_{93}=-0.030206751\) \(a_{94}=+0.298598911\) \(a_{95}=+0.023144046\)
\(a_{96}=+0.102062073\) \(a_{97}=-0.964294423\) \(a_{98}=+1.137666813\) \(a_{99}=-0.598484469\) \(a_{100}=-0.499178767\)

Showing 100 of 1000 available coefficients

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