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: \( 10.1961201777 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.166094334\)
\(a_{6}=-0.408248290\) \(a_{7}=-1.221218091\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.824553211\)
\(a_{11}=+0.666338978\) \(a_{12}=+0.288675135\) \(a_{13}=+1.108435319\) \(a_{14}=+0.863531594\) \(a_{15}=+0.673244878\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.810840873\) \(a_{18}=-0.235702260\) \(a_{19}=+1.819394054\) \(a_{20}=+0.583047167\)
\(a_{21}=-0.705070594\) \(a_{22}=-0.471172810\) \(a_{23}=+0.908169653\) \(a_{24}=-0.204124145\) \(a_{25}=+0.359775996\)
\(a_{26}=-0.783782131\) \(a_{27}=+0.192450090\) \(a_{28}=-0.610609046\) \(a_{29}=+0.557449988\) \(a_{30}=-0.476056018\)
\(a_{31}=+1.224042451\) \(a_{32}=-0.176776695\) \(a_{33}=+0.384710988\) \(a_{34}=+0.573351080\) \(a_{35}=-1.424055497\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.057118033\) \(a_{38}=-1.286505873\) \(a_{39}=+0.639955430\) \(a_{40}=-0.412276606\)
\(a_{41}=-0.009754424\) \(a_{42}=+0.498560198\) \(a_{43}=+1.354781265\) \(a_{44}=+0.333169489\) \(a_{45}=+0.388698111\)
\(a_{46}=-0.642172920\) \(a_{47}=-1.368771077\) \(a_{48}=+0.144337567\) \(a_{49}=+0.491373627\) \(a_{50}=-0.254400046\)
\(a_{51}=-0.468139196\) \(a_{52}=+0.554217660\) \(a_{53}=-1.378277810\) \(a_{54}=-0.136082763\) \(a_{55}=+0.777014106\)
\(a_{56}=+0.431765797\) \(a_{57}=+1.050427647\) \(a_{58}=-0.394176666\) \(a_{59}=+0.281800500\) \(a_{60}=+0.336622439\)
\(a_{61}=-0.041797000\) \(a_{62}=-0.865528717\) \(a_{63}=-0.407072697\) \(a_{64}=+0.125000000\) \(a_{65}=+1.292540146\)
\(a_{66}=-0.272031748\) \(a_{67}=-1.819828000\) \(a_{68}=-0.405420437\) \(a_{69}=+0.524331994\) \(a_{70}=+1.006959299\)
\(a_{71}=-0.571799994\) \(a_{72}=-0.117851130\) \(a_{73}=+0.168149993\) \(a_{74}=-0.040388548\) \(a_{75}=+0.207716768\)
\(a_{76}=+0.909697027\) \(a_{77}=-0.813745214\) \(a_{78}=-0.452516824\) \(a_{79}=+0.805999756\) \(a_{80}=+0.291523583\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.006897419\) \(a_{83}=+1.315002441\) \(a_{84}=-0.352535297\) \(a_{85}=-0.945516948\)
\(a_{86}=-0.957975019\) \(a_{87}=+0.321843900\) \(a_{88}=-0.235586405\) \(a_{89}=-1.020004272\) \(a_{90}=-0.274851070\)
\(a_{91}=-1.353641265\) \(a_{92}=+0.454084827\) \(a_{93}=+0.706701238\) \(a_{94}=+0.967867310\) \(a_{95}=+2.121585098\)
\(a_{96}=-0.102062073\)

Showing all 96 available coefficients

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