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: \( 17.1404035238 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.691665466\)
\(a_{6}=-0.408248290\) \(a_{7}=+0.926251529\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.489081342\)
\(a_{11}=-0.448009691\) \(a_{12}=+0.288675135\) \(a_{13}=-1.559444973\) \(a_{14}=-0.654958737\) \(a_{15}=-0.399333243\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.680022963\) \(a_{18}=-0.235702260\) \(a_{19}=-0.551024411\) \(a_{20}=-0.345832733\)
\(a_{21}=+0.534771569\) \(a_{22}=+0.316790690\) \(a_{23}=+0.758365754\) \(a_{24}=-0.204124145\) \(a_{25}=-0.521598883\)
\(a_{26}=+1.102694116\) \(a_{27}=+0.192450090\) \(a_{28}=+0.463125764\) \(a_{29}=+0.970295054\) \(a_{30}=+0.282371244\)
\(a_{31}=-0.060932291\) \(a_{32}=-0.176776695\) \(a_{33}=-0.258658515\) \(a_{34}=-1.187955630\) \(a_{35}=-0.640656195\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.927472741\) \(a_{38}=+0.389633098\) \(a_{39}=-0.900345975\) \(a_{40}=+0.244540671\)
\(a_{41}=-1.358419164\) \(a_{42}=-0.378140603\) \(a_{43}=-0.552452299\) \(a_{44}=-0.224004845\) \(a_{45}=-0.230555155\)
\(a_{46}=-0.536245568\) \(a_{47}=-1.153539908\) \(a_{48}=+0.144337567\) \(a_{49}=-0.142058106\) \(a_{50}=+0.368826107\)
\(a_{51}=+0.969961710\) \(a_{52}=-0.779722487\) \(a_{53}=-0.554754226\) \(a_{54}=-0.136082763\) \(a_{55}=+0.309872832\)
\(a_{56}=-0.327479368\) \(a_{57}=-0.318134092\) \(a_{58}=-0.686102212\) \(a_{59}=+1.363457383\) \(a_{60}=-0.199666622\)
\(a_{61}=-1.644378610\) \(a_{62}=+0.043085636\) \(a_{63}=+0.308750510\) \(a_{64}=+0.125000000\) \(a_{65}=+1.078614235\)
\(a_{66}=+0.182899190\) \(a_{67}=-0.600995550\) \(a_{68}=+0.840011482\) \(a_{69}=+0.437842672\) \(a_{70}=+0.453012340\)
\(a_{71}=-1.680744200\) \(a_{72}=-0.117851130\) \(a_{73}=-1.434658200\) \(a_{74}=+0.655822264\) \(a_{75}=-0.301145255\)
\(a_{76}=-0.275512206\) \(a_{77}=-0.414969661\) \(a_{78}=+0.636640744\) \(a_{79}=+1.907151997\) \(a_{80}=-0.172916367\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.960547403\) \(a_{83}=-1.123560000\) \(a_{84}=+0.267385785\) \(a_{85}=-1.162013866\)
\(a_{86}=+0.390642767\) \(a_{87}=+0.560200111\) \(a_{88}=+0.158395345\) \(a_{89}=-1.066499949\) \(a_{90}=+0.163027114\)
\(a_{91}=-1.444438290\) \(a_{92}=+0.379182877\) \(a_{93}=-0.035179275\) \(a_{94}=+0.815675891\) \(a_{95}=+0.381124556\)
\(a_{96}=-0.102062073\) \(a_{97}=+0.215999603\) \(a_{98}=+0.100450250\) \(a_{99}=-0.149336564\) \(a_{100}=-0.260799441\)

Showing 100 of 106 available coefficients

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