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: \( 31.1202312685 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.873110012\) \(a_{3}=-0.577350269\) \(a_{4}=+2.508541117\) \(a_{5}=-0.259282668\)
\(a_{6}=-1.081440570\) \(a_{7}=-1.446560734\) \(a_{8}=+2.825663470\) \(a_{9}=+0.333333333\) \(a_{10}=-0.485664962\)
\(a_{11}=+0.003434908\) \(a_{12}=-1.448306889\) \(a_{13}=+0.356530386\) \(a_{14}=-2.709567394\) \(a_{15}=+0.149696918\)
\(a_{16}=+2.784237418\) \(a_{17}=+1.653840925\) \(a_{18}=+0.624370004\) \(a_{19}=+1.089055166\) \(a_{20}=-0.650421234\)
\(a_{21}=+0.835172229\) \(a_{22}=+0.006433961\) \(a_{23}=+1.297407815\) \(a_{24}=-1.631397565\) \(a_{25}=-0.932772498\)
\(a_{26}=+0.667820636\) \(a_{27}=-0.192450090\) \(a_{28}=-3.628757080\) \(a_{29}=+1.554480392\) \(a_{30}=+0.280398796\)
\(a_{31}=+0.236765711\) \(a_{32}=+2.389519515\) \(a_{33}=-0.001983145\) \(a_{34}=+3.097825995\) \(a_{35}=+0.375068127\)
\(a_{36}=+0.836180372\) \(a_{37}=-0.800388501\) \(a_{38}=+2.039920136\) \(a_{39}=-0.205842914\) \(a_{40}=-0.732645564\)
\(a_{41}=+0.106878512\) \(a_{42}=+1.564369465\) \(a_{43}=+0.198170892\) \(a_{44}=+0.008616609\) \(a_{45}=-0.086427556\)
\(a_{46}=+2.430187568\) \(a_{47}=-0.051648624\) \(a_{48}=-1.607480223\) \(a_{49}=+1.092537958\) \(a_{50}=-1.747185505\)
\(a_{51}=-0.954845503\) \(a_{52}=+0.894371133\) \(a_{53}=+0.772755858\) \(a_{54}=-0.360480190\) \(a_{55}=-0.000890612\)
\(a_{56}=-4.087493824\) \(a_{57}=-0.628766294\) \(a_{58}=+2.911712786\) \(a_{59}=+0.855529741\) \(a_{60}=+0.375520874\)
\(a_{61}=-0.181693570\) \(a_{62}=+0.443488224\) \(a_{63}=-0.482186911\) \(a_{64}=+1.691595508\) \(a_{65}=-0.092442150\)
\(a_{66}=-0.003714649\) \(a_{67}=-0.462649408\) \(a_{68}=+4.148727961\) \(a_{69}=-0.749058751\) \(a_{70}=+0.702543863\)
\(a_{71}=+0.430035466\) \(a_{72}=+0.941887823\) \(a_{73}=-0.138737447\) \(a_{74}=-1.499215715\) \(a_{75}=+0.538536453\)
\(a_{76}=+2.731939664\) \(a_{77}=-0.004968803\) \(a_{78}=-0.385566424\) \(a_{79}=+0.712956307\) \(a_{80}=-0.721904506\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.200195212\) \(a_{83}=-0.312542340\) \(a_{84}=+2.095063877\) \(a_{85}=-0.428812288\)
\(a_{86}=+0.371195883\) \(a_{87}=-0.897479673\) \(a_{88}=+0.009705895\) \(a_{89}=-1.109573768\) \(a_{90}=-0.161888321\)
\(a_{91}=-0.515742857\) \(a_{92}=+3.254600850\) \(a_{93}=-0.136696747\) \(a_{94}=-0.096743555\) \(a_{95}=-0.282373129\)
\(a_{96}=-1.379589735\) \(a_{97}=+0.010836079\) \(a_{98}=+2.046443788\) \(a_{99}=+0.001144969\) \(a_{100}=-2.339898164\)

Showing 100 of 1228 available coefficients

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