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: \( 26.4529566231 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.037010177\) \(a_{3}=+0.577350269\) \(a_{4}=-0.998630247\) \(a_{5}=-0.690089283\)
\(a_{6}=+0.021367836\) \(a_{7}=+1.306032951\) \(a_{8}=-0.073969660\) \(a_{9}=+0.333333333\) \(a_{10}=-0.025540327\)
\(a_{11}=-1.030675923\) \(a_{12}=-0.576559442\) \(a_{13}=-1.037360524\) \(a_{14}=+0.048336511\) \(a_{15}=-0.398423233\)
\(a_{16}=+0.995892617\) \(a_{17}=+0.516180804\) \(a_{18}=+0.012336726\) \(a_{19}=-1.040263281\) \(a_{20}=+0.689144031\)
\(a_{21}=+0.754038476\) \(a_{22}=-0.038145499\) \(a_{23}=+0.059158216\) \(a_{24}=-0.042706403\) \(a_{25}=-0.523776782\)
\(a_{26}=-0.038392897\) \(a_{27}=+0.192450090\) \(a_{28}=-1.304244008\) \(a_{29}=+1.620817002\) \(a_{30}=-0.014745715\)
\(a_{31}=+1.062496686\) \(a_{32}=+0.110827822\) \(a_{33}=-0.595061022\) \(a_{34}=+0.019103943\) \(a_{35}=-0.901279342\)
\(a_{36}=-0.332876749\) \(a_{37}=-0.132654194\) \(a_{38}=-0.038500328\) \(a_{39}=-0.598920378\) \(a_{40}=+0.051045670\)
\(a_{41}=-1.166900296\) \(a_{42}=+0.027907098\) \(a_{43}=+1.940649368\) \(a_{44}=+1.029264152\) \(a_{45}=-0.230029761\)
\(a_{46}=+0.002189456\) \(a_{47}=+1.289780635\) \(a_{48}=+0.574978870\) \(a_{49}=+0.705722069\) \(a_{50}=-0.019385072\)
\(a_{51}=+0.298017126\) \(a_{52}=+1.035939596\) \(a_{53}=+1.320800950\) \(a_{54}=+0.007122612\) \(a_{55}=+0.711258409\)
\(a_{56}=-0.096606813\) \(a_{57}=-0.600596285\) \(a_{58}=+0.059986725\) \(a_{59}=+0.207677827\) \(a_{60}=+0.397877492\)
\(a_{61}=+0.989785693\) \(a_{62}=+0.039323191\) \(a_{63}=+0.435344317\) \(a_{64}=-0.991790859\) \(a_{65}=+0.715871380\)
\(a_{66}=-0.022023314\) \(a_{67}=-0.298292248\) \(a_{68}=-0.515473764\) \(a_{69}=+0.034155012\) \(a_{70}=-0.033356508\)
\(a_{71}=+0.690245081\) \(a_{72}=-0.024656553\) \(a_{73}=+0.458814018\) \(a_{74}=-0.004909555\) \(a_{75}=-0.302402666\)
\(a_{76}=+1.038838377\) \(a_{77}=-1.346096718\) \(a_{78}=-0.022166149\) \(a_{79}=-0.033808955\) \(a_{80}=-0.687254821\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.043187187\) \(a_{83}=+1.897754201\) \(a_{84}=-0.753005629\) \(a_{85}=-0.356210841\)
\(a_{86}=+0.071823777\) \(a_{87}=+0.935779132\) \(a_{88}=+0.076238747\) \(a_{89}=-0.744545221\) \(a_{90}=-0.008513442\)
\(a_{91}=-1.354827026\) \(a_{92}=-0.059077184\) \(a_{93}=+0.613432748\) \(a_{94}=+0.047735010\) \(a_{95}=+0.717874541\)
\(a_{96}=+0.063986473\) \(a_{97}=-0.094415165\) \(a_{98}=+0.026118899\) \(a_{99}=-0.343558641\) \(a_{100}=+0.523059337\)

Showing 100 of 1228 available coefficients

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