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: \( 19.8961039469 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.606473332\) \(a_{3}=-0.577350269\) \(a_{4}=+1.580756566\) \(a_{5}=-1.077342070\)
\(a_{6}=+0.927497811\) \(a_{7}=+1.190012413\) \(a_{8}=-0.932969936\) \(a_{9}=+0.333333333\) \(a_{10}=+1.730721305\)
\(a_{11}=-1.376616632\) \(a_{12}=-0.912650229\) \(a_{13}=-0.964527289\) \(a_{14}=-1.911723207\) \(a_{15}=+0.622003734\)
\(a_{16}=-0.081965245\) \(a_{17}=-1.082878494\) \(a_{18}=-0.535491111\) \(a_{19}=+0.224818528\) \(a_{20}=-1.703015552\)
\(a_{21}=-0.687053987\) \(a_{22}=+2.211497908\) \(a_{23}=-0.879648228\) \(a_{24}=+0.538650444\) \(a_{25}=+0.160665936\)
\(a_{26}=+1.549487367\) \(a_{27}=-0.192450090\) \(a_{28}=+1.881119936\) \(a_{29}=+1.272266400\) \(a_{30}=-0.999232411\)
\(a_{31}=-0.724180797\) \(a_{32}=+1.064644916\) \(a_{33}=+0.794789983\) \(a_{34}=+1.739615423\) \(a_{35}=-1.282050437\)
\(a_{36}=+0.526918855\) \(a_{37}=-0.871616762\) \(a_{38}=-0.361164969\) \(a_{39}=+0.556870090\) \(a_{40}=+1.005127762\)
\(a_{41}=-1.051376044\) \(a_{42}=+1.103733908\) \(a_{43}=+0.987053044\) \(a_{44}=-2.176095781\) \(a_{45}=-0.359114023\)
\(a_{46}=+1.413131420\) \(a_{47}=-0.646183942\) \(a_{48}=+0.047322656\) \(a_{49}=+0.416129544\) \(a_{50}=-0.258105542\)
\(a_{51}=+0.625200190\) \(a_{52}=-1.524682845\) \(a_{53}=+0.801911416\) \(a_{54}=+0.309165937\) \(a_{55}=+1.483087013\)
\(a_{56}=-1.110245805\) \(a_{57}=-0.129799037\) \(a_{58}=-2.043862043\) \(a_{59}=-0.198691926\) \(a_{60}=+0.983236487\)
\(a_{61}=+1.002845862\) \(a_{62}=+1.163377138\) \(a_{63}=+0.396670804\) \(a_{64}=-1.628358420\) \(a_{65}=+1.039125826\)
\(a_{66}=-1.276808913\) \(a_{67}=+0.007977301\) \(a_{68}=-1.711767290\) \(a_{69}=+0.507865141\) \(a_{70}=+2.059579837\)
\(a_{71}=-1.056951444\) \(a_{72}=-0.310989979\) \(a_{73}=+0.655702312\) \(a_{74}=+1.400229085\) \(a_{75}=-0.092760522\)
\(a_{76}=+0.355383364\) \(a_{77}=-1.638190881\) \(a_{78}=-0.894596948\) \(a_{79}=-0.346729765\) \(a_{80}=+0.088304606\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.689007576\) \(a_{83}=+0.240904017\) \(a_{84}=-1.086065102\) \(a_{85}=+1.166630559\)
\(a_{86}=-1.585674393\) \(a_{87}=-0.734543349\) \(a_{88}=+1.284341931\) \(a_{89}=+1.088424494\) \(a_{90}=+0.576907102\)
\(a_{91}=-1.147799446\) \(a_{92}=-1.390509712\) \(a_{93}=+0.418105978\) \(a_{94}=+1.038077271\) \(a_{95}=-0.242206458\)
\(a_{96}=-0.614673029\) \(a_{97}=+0.223098479\) \(a_{98}=-0.668501015\) \(a_{99}=-0.458872211\) \(a_{100}=+0.253973734\)

Showing 100 of 1228 available coefficients

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