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: \( 10.2310756893 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.780192370\) \(a_{3}=+0.577350269\) \(a_{4}=+2.169084875\) \(a_{5}=-0.275771013\)
\(a_{6}=-1.027794544\) \(a_{7}=+0.312473251\) \(a_{8}=-2.081195975\) \(a_{9}=+0.333333333\) \(a_{10}=+0.490925453\)
\(a_{11}=-1.502805725\) \(a_{12}=+1.252321737\) \(a_{13}=-0.508311113\) \(a_{14}=-0.556262498\) \(a_{15}=-0.159216469\)
\(a_{16}=+1.535844320\) \(a_{17}=-0.461202482\) \(a_{18}=-0.593397457\) \(a_{19}=-0.207751812\) \(a_{20}=-0.598170733\)
\(a_{21}=+0.180406516\) \(a_{22}=+2.675283285\) \(a_{23}=-1.040153810\) \(a_{24}=-1.201579056\) \(a_{25}=-0.923950348\)
\(a_{26}=+0.904891566\) \(a_{27}=+0.192450090\) \(a_{28}=+0.677781003\) \(a_{29}=-0.550707398\) \(a_{30}=+0.283435943\)
\(a_{31}=+0.413103356\) \(a_{32}=-0.652902366\) \(a_{33}=-0.867645290\) \(a_{34}=+0.821029140\) \(a_{35}=-0.086171065\)
\(a_{36}=+0.723028292\) \(a_{37}=-1.328530914\) \(a_{38}=+0.369838191\) \(a_{39}=-0.293473558\) \(a_{40}=+0.573933522\)
\(a_{41}=+1.976304621\) \(a_{42}=-0.321158303\) \(a_{43}=-0.594045770\) \(a_{44}=-3.259713168\) \(a_{45}=-0.091923671\)
\(a_{46}=+1.851673877\) \(a_{47}=+0.460685613\) \(a_{48}=+0.886720132\) \(a_{49}=-0.902360467\) \(a_{50}=+1.644809361\)
\(a_{51}=-0.266275377\) \(a_{52}=-1.102569948\) \(a_{53}=-0.668229743\) \(a_{54}=-0.342598181\) \(a_{55}=+0.414430257\)
\(a_{56}=-0.650318073\) \(a_{57}=-0.119945565\) \(a_{58}=+0.980365108\) \(a_{59}=+1.345668442\) \(a_{60}=-0.345354034\)
\(a_{61}=-0.301547770\) \(a_{62}=-0.735403442\) \(a_{63}=+0.104157750\) \(a_{64}=-0.373552510\) \(a_{65}=+0.140177471\)
\(a_{66}=+1.544575525\) \(a_{67}=-0.234199365\) \(a_{68}=-1.000387329\) \(a_{69}=-0.600533082\) \(a_{70}=+0.153401073\)
\(a_{71}=-0.522951244\) \(a_{72}=-0.693731992\) \(a_{73}=+0.696026086\) \(a_{74}=+2.365040596\) \(a_{75}=-0.533442982\)
\(a_{76}=-0.450631314\) \(a_{77}=-0.469586591\) \(a_{78}=+0.522439389\) \(a_{79}=+1.506470529\) \(a_{80}=-0.423541344\)
\(a_{81}=+0.111111111\) \(a_{82}=-3.518202408\) \(a_{83}=-0.502840344\) \(a_{84}=+0.391317045\) \(a_{85}=+0.127186276\)
\(a_{86}=+1.057515747\) \(a_{87}=-0.317951064\) \(a_{88}=+3.127633225\) \(a_{89}=-0.072635010\) \(a_{90}=+0.163641818\)
\(a_{91}=-0.158833626\) \(a_{92}=-2.256181898\) \(a_{93}=+0.238505334\) \(a_{94}=-0.820109013\) \(a_{95}=+0.057291928\)
\(a_{96}=-0.376953357\) \(a_{97}=+0.864572631\) \(a_{98}=+1.606375219\) \(a_{99}=-0.500935242\) \(a_{100}=-2.004126726\)

Showing 100 of 1228 available coefficients

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