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: \( 27.683289262 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.637463416\) \(a_{3}=-0.577350269\) \(a_{4}=-0.593640393\) \(a_{5}=+1.817172226\)
\(a_{6}=-0.368039675\) \(a_{7}=+1.257072547\) \(a_{8}=-1.015887449\) \(a_{9}=+0.333333333\) \(a_{10}=+1.158380815\)
\(a_{11}=+1.054981571\) \(a_{12}=+0.342738441\) \(a_{13}=-0.264408121\) \(a_{14}=+0.801337760\) \(a_{15}=-1.049144874\)
\(a_{16}=-0.053950691\) \(a_{17}=-0.406634233\) \(a_{18}=+0.212487805\) \(a_{19}=-0.186320182\) \(a_{20}=-1.078746834\)
\(a_{21}=-0.725771173\) \(a_{22}=+0.672512157\) \(a_{23}=-1.256429299\) \(a_{24}=+0.586522892\) \(a_{25}=+2.302114900\)
\(a_{26}=-0.168550504\) \(a_{27}=-0.192450090\) \(a_{28}=-0.746249041\) \(a_{29}=+1.066952362\) \(a_{30}=-0.668791476\)
\(a_{31}=+0.709407539\) \(a_{32}=+0.981495857\) \(a_{33}=-0.609093894\) \(a_{34}=-0.259214447\) \(a_{35}=+2.284317319\)
\(a_{36}=-0.197880131\) \(a_{37}=-0.656239530\) \(a_{38}=-0.118772300\) \(a_{39}=+0.152656100\) \(a_{40}=-1.846042458\)
\(a_{41}=-0.030983184\) \(a_{42}=-0.462652572\) \(a_{43}=+0.558053278\) \(a_{44}=-0.626279674\) \(a_{45}=+0.605724075\)
\(a_{46}=-0.800927714\) \(a_{47}=+0.688793174\) \(a_{48}=+0.031148446\) \(a_{49}=+0.580231388\) \(a_{50}=+1.467514029\)
\(a_{51}=+0.234770384\) \(a_{52}=+0.156963341\) \(a_{53}=+1.705329266\) \(a_{54}=-0.122679892\) \(a_{55}=+1.917083210\)
\(a_{56}=-1.277044223\) \(a_{57}=+0.107572007\) \(a_{58}=+0.680143098\) \(a_{59}=+1.320423880\) \(a_{60}=+0.622814775\)
\(a_{61}=-0.225283552\) \(a_{62}=+0.452221354\) \(a_{63}=+0.419024182\) \(a_{64}=+0.679618394\) \(a_{65}=-0.480475094\)
\(a_{66}=-0.388275075\) \(a_{67}=-0.966947007\) \(a_{68}=+0.241394506\) \(a_{69}=+0.725399794\) \(a_{70}=+1.456168722\)
\(a_{71}=+0.542440534\) \(a_{72}=-0.338629150\) \(a_{73}=-0.310811945\) \(a_{74}=-0.418328693\) \(a_{75}=-1.329126657\)
\(a_{76}=+0.110607186\) \(a_{77}=+1.326188371\) \(a_{78}=+0.097312679\) \(a_{79}=-0.451230983\) \(a_{80}=-0.098037698\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.019750647\) \(a_{83}=+0.786432583\) \(a_{84}=+0.430847084\) \(a_{85}=-0.738924434\)
\(a_{86}=+0.355738549\) \(a_{87}=-0.616005233\) \(a_{88}=-1.071742537\) \(a_{89}=+0.519695646\) \(a_{90}=+0.386126938\)
\(a_{91}=-0.332380190\) \(a_{92}=+0.745867183\) \(a_{93}=-0.409576634\) \(a_{94}=+0.439080450\) \(a_{95}=-0.338575860\)
\(a_{96}=-0.566666897\) \(a_{97}=+1.402857549\) \(a_{98}=+0.369876283\) \(a_{99}=+0.351660524\) \(a_{100}=-1.366628393\)

Showing 100 of 1228 available coefficients

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