Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 31.63446345 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.999740987\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.706923631\) \(a_{7}=+0.124293464\) \(a_{8}=-0.353553391\) \(a_{9}=-0.000517960\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.353588895\) \(a_{12}=+0.499870493\) \(a_{13}=+1.677157154\) \(a_{14}=-0.087888751\) \(a_{15}=+0.447097761\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.387565457\) \(a_{18}=+0.000366253\) \(a_{19}=+1.455604309\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.124261271\) \(a_{22}=-0.250025106\) \(a_{23}=+1.791277312\) \(a_{24}=-0.353461816\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.185929196\) \(a_{27}=-1.000258812\) \(a_{28}=+0.062146732\) \(a_{29}=+1.853765375\) \(a_{30}=-0.316145859\)
\(a_{31}=-0.131788408\) \(a_{32}=-0.176776695\) \(a_{33}=+0.353497311\) \(a_{34}=-0.981156944\) \(a_{35}=+0.055585727\)
\(a_{36}=-0.000258980\) \(a_{37}=-0.515010061\) \(a_{38}=-1.029267678\) \(a_{39}=+1.676722747\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.301918649\) \(a_{42}=-0.087865987\) \(a_{43}=-1.258132968\) \(a_{44}=+0.176794448\) \(a_{45}=-0.000231639\)
\(a_{46}=-1.266624334\) \(a_{47}=+1.524849120\) \(a_{48}=+0.249935247\) \(a_{49}=-0.984551135\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.387206059\) \(a_{52}=+0.838578577\) \(a_{53}=-0.506650833\) \(a_{54}=+0.707289789\) \(a_{55}=+0.158129761\)
\(a_{56}=-0.043944376\) \(a_{57}=+1.455227288\) \(a_{58}=-1.310810067\) \(a_{59}=-0.381723586\) \(a_{60}=+0.223548881\)
\(a_{61}=-0.927094822\) \(a_{62}=+0.093188477\) \(a_{63}=-0.000064379\) \(a_{64}=+0.125000000\) \(a_{65}=+0.750047481\)
\(a_{66}=-0.249960346\) \(a_{67}=-1.078392850\) \(a_{68}=+0.693782729\) \(a_{69}=+1.790813347\) \(a_{70}=-0.039305045\)
\(a_{71}=-0.150794959\) \(a_{72}=+0.000183126\) \(a_{73}=+1.439256293\) \(a_{74}=+0.364167106\) \(a_{75}=+0.199948197\)
\(a_{76}=+0.727802155\) \(a_{77}=+0.043948789\) \(a_{78}=-1.185622025\) \(a_{79}=-0.510403833\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.999481772\) \(a_{82}=+0.213488724\) \(a_{83}=+1.566988946\) \(a_{84}=+0.062130635\) \(a_{85}=+0.620538137\)
\(a_{86}=+0.889634354\) \(a_{87}=+1.853285225\) \(a_{88}=-0.125012553\) \(a_{89}=+0.177064281\) \(a_{90}=+0.000163793\)
\(a_{91}=+0.208459673\) \(a_{92}=+0.895638656\) \(a_{93}=-0.131754273\) \(a_{94}=-1.078231153\) \(a_{95}=+0.650966037\)
\(a_{96}=-0.176730908\) \(a_{97}=+0.930386363\) \(a_{98}=+0.696182784\) \(a_{99}=-0.000183145\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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