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: \( 16.7362155908 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.847947276\) \(a_{3}=-0.577350269\) \(a_{4}=+2.414909136\) \(a_{5}=+0.958173287\)
\(a_{6}=+1.066912857\) \(a_{7}=+0.941696536\) \(a_{8}=-2.614677485\) \(a_{9}=+0.333333333\) \(a_{10}=-1.770653716\)
\(a_{11}=-0.409513048\) \(a_{12}=-1.394248440\) \(a_{13}=+0.483116897\) \(a_{14}=-1.740205549\) \(a_{15}=-0.553201605\)
\(a_{16}=+2.416877001\) \(a_{17}=+0.412473153\) \(a_{18}=-0.615982425\) \(a_{19}=+0.718855890\) \(a_{20}=+2.313901425\)
\(a_{21}=-0.543688748\) \(a_{22}=+0.756758521\) \(a_{23}=-0.496736965\) \(a_{24}=+1.509584750\) \(a_{25}=-0.081903952\)
\(a_{26}=-0.892774554\) \(a_{27}=-0.192450090\) \(a_{28}=+2.274111568\) \(a_{29}=-1.915951626\) \(a_{30}=+1.022287400\)
\(a_{31}=+0.908411935\) \(a_{32}=-1.851583786\) \(a_{33}=+0.236432468\) \(a_{34}=-0.762228640\) \(a_{35}=+0.902308465\)
\(a_{36}=+0.804969712\) \(a_{37}=+1.370225037\) \(a_{38}=-1.328407784\) \(a_{39}=-0.278927670\) \(a_{40}=-2.505314121\)
\(a_{41}=+1.347821953\) \(a_{42}=+1.004708142\) \(a_{43}=+0.739802189\) \(a_{44}=-0.988936800\) \(a_{45}=+0.319391096\)
\(a_{46}=+0.917943722\) \(a_{47}=-0.362897099\) \(a_{48}=-1.395384587\) \(a_{49}=-0.113207634\) \(a_{50}=+0.151354185\)
\(a_{51}=-0.238141486\) \(a_{52}=+1.166683408\) \(a_{53}=+0.420358226\) \(a_{54}=+0.355637619\) \(a_{55}=-0.392384463\)
\(a_{56}=-2.462232730\) \(a_{57}=-0.415031642\) \(a_{58}=+3.540577589\) \(a_{59}=+1.115709764\) \(a_{60}=-1.335931611\)
\(a_{61}=-1.322088489\) \(a_{62}=-1.678697360\) \(a_{63}=+0.313898845\) \(a_{64}=+1.004752213\) \(a_{65}=+0.462909705\)
\(a_{66}=-0.436914736\) \(a_{67}=+1.120848398\) \(a_{68}=+0.996085185\) \(a_{69}=+0.286791221\) \(a_{70}=-1.667418471\)
\(a_{71}=-0.134623280\) \(a_{72}=-0.871559162\) \(a_{73}=+1.405743732\) \(a_{74}=-2.532103625\) \(a_{75}=+0.047287269\)
\(a_{76}=+1.735971657\) \(a_{77}=-0.385637018\) \(a_{78}=+0.515443629\) \(a_{79}=+0.036897035\) \(a_{80}=+2.315786980\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.490703908\) \(a_{83}=+0.371881399\) \(a_{84}=-1.312958926\) \(a_{85}=+0.395220757\)
\(a_{86}=-1.367115441\) \(a_{87}=+1.106175187\) \(a_{88}=+1.070744545\) \(a_{89}=+0.598066034\) \(a_{90}=-0.590217905\)
\(a_{91}=+0.454949508\) \(a_{92}=-1.199574635\) \(a_{93}=-0.524471875\) \(a_{94}=+0.670614706\) \(a_{95}=+0.688788511\)
\(a_{96}=+1.069012397\) \(a_{97}=-1.269464456\) \(a_{98}=+0.209201740\) \(a_{99}=-0.136504349\) \(a_{100}=-0.197790601\)

Showing 100 of 1228 available coefficients

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