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: \( 5.09874190873 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.342406732\) \(a_{3}=-0.577350269\) \(a_{4}=+0.802055834\) \(a_{5}=-0.062485317\)
\(a_{6}=-0.775038885\) \(a_{7}=+0.753838133\) \(a_{8}=-0.265721492\) \(a_{9}=+0.333332814\) \(a_{10}=-0.083877677\)
\(a_{11}=-0.408349072\) \(a_{12}=-0.463067152\) \(a_{13}=+0.527645079\) \(a_{14}=+1.011957405\) \(a_{15}=+0.036075914\)
\(a_{16}=-1.158762273\) \(a_{17}=-0.967583198\) \(a_{18}=+0.447468911\) \(a_{19}=+1.560205625\) \(a_{20}=-0.050116712\)
\(a_{21}=-0.435228658\) \(a_{22}=-0.548146759\) \(a_{23}=+0.285124950\) \(a_{24}=+0.153414426\) \(a_{25}=-0.996095585\)
\(a_{26}=+0.708314306\) \(a_{27}=-0.192450090\) \(a_{28}=+0.604620285\) \(a_{29}=-0.216424252\) \(a_{30}=+0.048428550\)
\(a_{31}=+1.154221603\) \(a_{32}=-1.289808695\) \(a_{33}=+0.235750217\) \(a_{34}=-1.298890198\) \(a_{35}=-0.047103815\)
\(a_{36}=+0.267351945\) \(a_{37}=+0.254344444\) \(a_{38}=+2.094430534\) \(a_{39}=-0.304636027\) \(a_{40}=+0.016603697\)
\(a_{41}=-1.105075659\) \(a_{42}=-0.584253882\) \(a_{43}=-0.126149776\) \(a_{44}=-0.327504542\) \(a_{45}=-0.020828441\)
\(a_{46}=+0.382753645\) \(a_{47}=+1.008106190\) \(a_{48}=+0.669011724\) \(a_{49}=-0.431728035\) \(a_{50}=-1.337165440\)
\(a_{51}=+0.558634402\) \(a_{52}=+0.423200841\) \(a_{53}=+0.247646995\) \(a_{54}=-0.258346253\) \(a_{55}=+0.025514612\)
\(a_{56}=-0.200311064\) \(a_{57}=-0.900785137\) \(a_{58}=-0.290529373\) \(a_{59}=+0.068951484\) \(a_{60}=+0.028934898\)
\(a_{61}=+0.485289997\) \(a_{62}=+1.549434850\) \(a_{63}=+0.251279382\) \(a_{64}=-0.572685603\) \(a_{65}=-0.032970069\)
\(a_{66}=+0.316472679\) \(a_{67}=-0.692441700\) \(a_{68}=-0.776055750\) \(a_{69}=-0.164616966\) \(a_{70}=-0.063232476\)
\(a_{71}=-1.106816140\) \(a_{72}=-0.088573862\) \(a_{73}=+1.507834832\) \(a_{74}=+0.341433699\) \(a_{75}=+0.575096057\)
\(a_{76}=+1.251372020\) \(a_{77}=-0.307815754\) \(a_{78}=-0.408945456\) \(a_{79}=-1.278016270\) \(a_{80}=+0.072405622\)
\(a_{81}=+0.111111099\) \(a_{82}=-1.483461002\) \(a_{83}=+1.611629488\) \(a_{84}=-0.349077669\) \(a_{85}=+0.060459685\)
\(a_{86}=-0.169344400\) \(a_{87}=+0.124952628\) \(a_{88}=+0.108502589\) \(a_{89}=-0.414761438\) \(a_{90}=-0.027960407\)
\(a_{91}=+0.397758954\) \(a_{92}=+0.228686241\) \(a_{93}=-0.666389909\) \(a_{94}=+1.353290009\) \(a_{95}=-0.097489589\)
\(a_{96}=+0.744671392\) \(a_{97}=-0.080276446\) \(a_{98}=-0.579554645\) \(a_{99}=-0.136110443\) \(a_{100}=-0.798924280\)

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