Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.0782262249 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.180587191\) \(a_{3}=+0.577350269\) \(a_{4}=+0.393786117\) \(a_{5}=-0.399500430\)
\(a_{6}=-0.681612333\) \(a_{7}=-1.323343169\) \(a_{8}=+0.715688346\) \(a_{9}=+0.333333333\) \(a_{10}=+0.471645091\)
\(a_{11}=+1.253310947\) \(a_{12}=+0.227352520\) \(a_{13}=-1.089786210\) \(a_{14}=+1.562321996\) \(a_{15}=-0.230651681\)
\(a_{16}=-1.238718611\) \(a_{17}=+0.344911753\) \(a_{18}=-0.393529064\) \(a_{19}=+0.615986312\) \(a_{20}=-0.157317723\)
\(a_{21}=-0.764032535\) \(a_{22}=-1.479642852\) \(a_{23}=-0.188950596\) \(a_{24}=+0.413202859\) \(a_{25}=-0.840399406\)
\(a_{26}=+1.286587641\) \(a_{27}=+0.192450090\) \(a_{28}=-0.521114168\) \(a_{29}=+1.084348500\) \(a_{30}=+0.272304420\)
\(a_{31}=+1.853414935\) \(a_{32}=+0.746726980\) \(a_{33}=+0.723599413\) \(a_{34}=-0.407198398\) \(a_{35}=+0.528676166\)
\(a_{36}=+0.131262039\) \(a_{37}=+0.265889541\) \(a_{38}=-0.727225551\) \(a_{39}=-0.629188362\) \(a_{40}=-0.285917802\)
\(a_{41}=-0.663951007\) \(a_{42}=+0.902007025\) \(a_{43}=+1.340179912\) \(a_{44}=+0.493536451\) \(a_{45}=-0.133166810\)
\(a_{46}=+0.223072654\) \(a_{47}=+0.509460081\) \(a_{48}=-0.715174524\) \(a_{49}=+0.751237144\) \(a_{50}=+0.992164775\)
\(a_{51}=+0.199134893\) \(a_{52}=-0.429142680\) \(a_{53}=-1.835562190\) \(a_{54}=-0.227204111\) \(a_{55}=-0.500698263\)
\(a_{56}=-0.947101284\) \(a_{57}=+0.355639863\) \(a_{58}=-1.280167950\) \(a_{59}=-0.243911164\) \(a_{60}=-0.090827430\)
\(a_{61}=-0.339413657\) \(a_{62}=-2.188117933\) \(a_{63}=-0.441114390\) \(a_{64}=+0.357142303\) \(a_{65}=+0.435370060\)
\(a_{66}=-0.854272199\) \(a_{67}=-1.404474616\) \(a_{68}=+0.135821460\) \(a_{69}=-0.109090678\) \(a_{70}=-0.624148310\)
\(a_{71}=+1.460694838\) \(a_{72}=+0.238562782\) \(a_{73}=-1.145648941\) \(a_{74}=-0.313905786\) \(a_{75}=-0.485204823\)
\(a_{76}=+0.242566858\) \(a_{77}=-1.658560481\) \(a_{78}=+0.742811721\) \(a_{79}=+0.643453017\) \(a_{80}=+0.494868618\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.783852055\) \(a_{83}=-0.679697844\) \(a_{84}=-0.300865405\) \(a_{85}=-0.137792394\)
\(a_{86}=-1.582199238\) \(a_{87}=+0.626048898\) \(a_{88}=+0.896980039\) \(a_{89}=-1.473946547\) \(a_{90}=+0.157215030\)
\(a_{91}=+1.442161137\) \(a_{92}=-0.074406122\) \(a_{93}=+1.070069612\) \(a_{94}=-0.601462046\) \(a_{95}=-0.246086797\)
\(a_{96}=+0.431123023\) \(a_{97}=-1.162132929\) \(a_{98}=-0.886900950\) \(a_{99}=+0.417770316\) \(a_{100}=-0.330937619\)

Showing 100 of 1228 available coefficients

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