Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 24.9166573879 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.675033201\) \(a_{3}=-0.577350269\) \(a_{4}=+1.805736223\) \(a_{5}=+1.715534726\)
\(a_{6}=+0.967080869\) \(a_{7}=-0.217246189\) \(a_{8}=-1.349634925\) \(a_{9}=+0.333333333\) \(a_{10}=-2.873577623\)
\(a_{11}=-1.430122870\) \(a_{12}=-1.042542295\) \(a_{13}=+1.023601860\) \(a_{14}=+0.363894579\) \(a_{15}=-0.990464436\)
\(a_{16}=+0.454947085\) \(a_{17}=-0.241566457\) \(a_{18}=-0.558344400\) \(a_{19}=-0.571345290\) \(a_{20}=+3.097803197\)
\(a_{21}=+0.125427146\) \(a_{22}=+2.395503289\) \(a_{23}=-0.200646680\) \(a_{24}=+0.779212087\) \(a_{25}=+1.943059397\)
\(a_{26}=-1.714567099\) \(a_{27}=-0.192450090\) \(a_{28}=-0.392289313\) \(a_{29}=+0.716233020\) \(a_{30}=+1.659060814\)
\(a_{31}=-0.874589426\) \(a_{32}=+0.587583453\) \(a_{33}=+0.825681824\) \(a_{34}=+0.404631836\) \(a_{35}=-0.372693381\)
\(a_{36}=+0.601912074\) \(a_{37}=-1.281950216\) \(a_{38}=+0.957022329\) \(a_{39}=-0.590976809\) \(a_{40}=-2.315345581\)
\(a_{41}=+0.429071325\) \(a_{42}=-0.210094633\) \(a_{43}=-0.725188671\) \(a_{44}=-2.582424671\) \(a_{45}=+0.571844909\)
\(a_{46}=+0.336089851\) \(a_{47}=+0.160649744\) \(a_{48}=-0.262663822\) \(a_{49}=-0.952804093\) \(a_{50}=-3.254689001\)
\(a_{51}=+0.139468459\) \(a_{52}=+1.848354956\) \(a_{53}=+1.228483234\) \(a_{54}=+0.322360290\) \(a_{55}=-2.453425447\)
\(a_{56}=+0.293203044\) \(a_{57}=+0.329866357\) \(a_{58}=-1.199714088\) \(a_{59}=+0.751111902\) \(a_{60}=-1.788517510\)
\(a_{61}=+1.331677730\) \(a_{62}=+1.464966325\) \(a_{63}=-0.072415396\) \(a_{64}=-1.439168877\) \(a_{65}=+1.756024536\)
\(a_{66}=-1.383044469\) \(a_{67}=-0.444907628\) \(a_{68}=-0.436205302\) \(a_{69}=+0.115843415\) \(a_{70}=+0.624273787\)
\(a_{71}=+0.607809260\) \(a_{72}=-0.449878308\) \(a_{73}=-0.773669247\) \(a_{74}=+2.147309174\) \(a_{75}=-1.121825866\)
\(a_{76}=-1.031698886\) \(a_{77}=+0.310688743\) \(a_{78}=+0.989905776\) \(a_{79}=-0.740998266\) \(a_{80}=+0.780477522\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.718708715\) \(a_{83}=-1.054277133\) \(a_{84}=+0.226488340\) \(a_{85}=-0.414415646\)
\(a_{86}=+1.214715101\) \(a_{87}=-0.413517327\) \(a_{88}=+1.930143773\) \(a_{89}=-0.036954091\) \(a_{90}=-0.957859208\)
\(a_{91}=-0.222373603\) \(a_{92}=-0.362314978\) \(a_{93}=+0.504944440\) \(a_{94}=-0.269093655\) \(a_{95}=-0.980162685\)
\(a_{96}=-0.339241465\) \(a_{97}=-1.177478559\) \(a_{98}=+1.595978490\) \(a_{99}=-0.476707623\) \(a_{100}=+3.508652737\)

Showing 100 of 1228 available coefficients

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