Properties

Level $47$
Weight $0$
Character 47.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 47 \)
Weight: \( 0 \)
Character: 47.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.73396081875 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.909295811\) \(a_{3}=+0.174853871\) \(a_{4}=-0.173181128\) \(a_{5}=+1.004955710\)
\(a_{6}=-0.158993893\) \(a_{7}=+0.525350640\) \(a_{8}=+1.066768685\) \(a_{9}=-0.969426124\) \(a_{10}=-0.913802017\)
\(a_{11}=-0.347309236\) \(a_{12}=-0.030281391\) \(a_{13}=-1.291885545\) \(a_{14}=-0.477699136\) \(a_{15}=+0.175720396\)
\(a_{16}=-0.796827169\) \(a_{17}=+0.750749533\) \(a_{18}=+0.881495113\) \(a_{19}=-1.002609568\) \(a_{20}=-0.174039363\)
\(a_{21}=+0.091859593\) \(a_{22}=+0.315806834\) \(a_{23}=+0.478228314\) \(a_{24}=+0.186528634\) \(a_{25}=+0.009935979\)
\(a_{26}=+1.174706115\) \(a_{27}=-0.344361782\) \(a_{28}=-0.090980816\) \(a_{29}=-1.129106233\) \(a_{30}=-0.159781820\)
\(a_{31}=-1.612582614\) \(a_{32}=-0.342217078\) \(a_{33}=-0.060728364\) \(a_{34}=-0.682653405\) \(a_{35}=+0.527954125\)
\(a_{36}=+0.167886310\) \(a_{37}=-0.317942175\) \(a_{38}=+0.911668680\) \(a_{39}=-0.225891189\) \(a_{40}=+1.072055281\)
\(a_{41}=-0.779298307\) \(a_{42}=-0.083527543\) \(a_{43}=+1.182904419\) \(a_{44}=+0.060147405\) \(a_{45}=-0.974230318\)
\(a_{46}=-0.434851003\) \(a_{47}=-0.145864992\) \(a_{48}=-0.139328315\) \(a_{49}=-0.724006705\) \(a_{50}=-0.009034744\)
\(a_{51}=+0.131271462\) \(a_{52}=+0.223730196\) \(a_{53}=+1.011483270\) \(a_{54}=+0.313126726\) \(a_{55}=-0.349030400\)
\(a_{56}=+0.560427612\) \(a_{57}=-0.175310164\) \(a_{58}=+1.026691567\) \(a_{59}=-1.698299509\) \(a_{60}=-0.030431456\)
\(a_{61}=-0.094282509\) \(a_{62}=+1.466314616\) \(a_{63}=-0.509288635\) \(a_{64}=+1.108003725\) \(a_{65}=-1.298287755\)
\(a_{66}=+0.055220047\) \(a_{67}=+1.828001933\) \(a_{68}=-0.130015651\) \(a_{69}=+0.083620072\) \(a_{70}=-0.480066475\)
\(a_{71}=+0.023906226\) \(a_{72}=-1.034153431\) \(a_{73}=-0.687183281\) \(a_{74}=+0.289103488\) \(a_{75}=+0.001737344\)
\(a_{76}=+0.173633056\) \(a_{77}=-0.182459130\) \(a_{78}=+0.205401912\) \(a_{79}=+0.482238277\) \(a_{80}=-0.800776013\)
\(a_{81}=+0.909213133\) \(a_{82}=+0.708612686\) \(a_{83}=-1.377654668\) \(a_{84}=-0.015908348\) \(a_{85}=+0.754470030\)
\(a_{86}=-1.075610033\) \(a_{87}=-0.197428596\) \(a_{88}=-0.370498617\) \(a_{89}=-0.380975009\) \(a_{90}=+0.885863547\)
\(a_{91}=-0.678692898\) \(a_{92}=-0.082820119\) \(a_{93}=-0.281966313\) \(a_{94}=+0.132634426\) \(a_{95}=-1.007578210\)
\(a_{96}=-0.059837981\) \(a_{97}=+0.592464301\) \(a_{98}=+0.658336264\) \(a_{99}=+0.336690647\) \(a_{100}=-0.001720724\)

Showing 100 of 546 available coefficients

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