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: \( 19.1759646544 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.791052197\) \(a_{3}=+0.577350269\) \(a_{4}=-0.374236421\) \(a_{5}=-1.376644885\)
\(a_{6}=-0.456714199\) \(a_{7}=-1.120328102\) \(a_{8}=+1.087092741\) \(a_{9}=+0.333333333\) \(a_{10}=+1.088997961\)
\(a_{11}=-1.715201466\) \(a_{12}=-0.216065498\) \(a_{13}=-0.447295292\) \(a_{14}=+0.886238007\) \(a_{15}=-0.794806295\)
\(a_{16}=-0.485710680\) \(a_{17}=-0.429433905\) \(a_{18}=-0.263684066\) \(a_{19}=-0.855966264\) \(a_{20}=+0.515190655\)
\(a_{21}=-0.646821731\) \(a_{22}=+1.356813889\) \(a_{23}=+0.710588306\) \(a_{24}=+0.627633286\) \(a_{25}=+0.895151139\)
\(a_{26}=+0.353833923\) \(a_{27}=+0.192450090\) \(a_{28}=+0.419267579\) \(a_{29}=+1.040356338\) \(a_{30}=+0.628733266\)
\(a_{31}=+0.627995143\) \(a_{32}=-0.702870240\) \(a_{33}=-0.990272028\) \(a_{34}=+0.339704635\) \(a_{35}=+1.542293951\)
\(a_{36}=-0.124745474\) \(a_{37}=-0.224851734\) \(a_{38}=+0.677113994\) \(a_{39}=-0.258246057\) \(a_{40}=-1.496540661\)
\(a_{41}=+0.312153900\) \(a_{42}=+0.511669752\) \(a_{43}=+0.281223739\) \(a_{44}=+0.641890858\) \(a_{45}=-0.458881628\)
\(a_{46}=-0.562112441\) \(a_{47}=+0.738916085\) \(a_{48}=-0.280425192\) \(a_{49}=+0.255135056\) \(a_{50}=-0.708111276\)
\(a_{51}=-0.247933781\) \(a_{52}=+0.167394189\) \(a_{53}=-0.048908695\) \(a_{54}=-0.152238066\) \(a_{55}=+2.361223325\)
\(a_{56}=-1.217900547\) \(a_{57}=-0.494192353\) \(a_{58}=-0.822976167\) \(a_{59}=+1.438563955\) \(a_{60}=+0.297445463\)
\(a_{61}=-1.495610277\) \(a_{62}=-0.496776938\) \(a_{63}=-0.373442701\) \(a_{64}=+1.041717728\) \(a_{65}=+0.615766776\)
\(a_{66}=+0.783356864\) \(a_{67}=-0.475127320\) \(a_{68}=+0.160709808\) \(a_{69}=+0.410258349\) \(a_{70}=-1.220035019\)
\(a_{71}=-0.212392374\) \(a_{72}=+0.362364247\) \(a_{73}=-1.531023515\) \(a_{74}=+0.177869458\) \(a_{75}=+0.516815751\)
\(a_{76}=+0.320333751\) \(a_{77}=+1.921588403\) \(a_{78}=+0.204286111\) \(a_{79}=-1.900502411\) \(a_{80}=+0.668651123\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.246930028\) \(a_{83}=-1.036812520\) \(a_{84}=+0.242064250\) \(a_{85}=+0.591177989\)
\(a_{86}=-0.222462656\) \(a_{87}=+0.600650012\) \(a_{88}=-1.864583062\) \(a_{89}=+0.868622545\) \(a_{90}=+0.362999320\)
\(a_{91}=+0.501117485\) \(a_{92}=-0.265928024\) \(a_{93}=+0.362573165\) \(a_{94}=-0.584521193\) \(a_{95}=+1.178361578\)
\(a_{96}=-0.405802322\) \(a_{97}=+0.061071386\) \(a_{98}=-0.201825147\) \(a_{99}=-0.571733822\) \(a_{100}=-0.334998159\)

Showing 100 of 1228 available coefficients

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