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: \( 23.425167202 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.473620500\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.334900267\) \(a_{7}=+1.494030640\) \(a_{8}=-0.353553391\) \(a_{9}=-0.775683622\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.480772155\) \(a_{12}=+0.236810250\) \(a_{13}=-1.627555339\) \(a_{14}=-1.056439197\) \(a_{15}=+0.211809527\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.180711994\) \(a_{18}=+0.548491149\) \(a_{19}=-0.372779118\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.707603539\) \(a_{22}=+0.339957251\) \(a_{23}=-0.752250871\) \(a_{24}=-0.167450134\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.150855417\) \(a_{27}=-0.841000165\) \(a_{28}=+0.747015320\) \(a_{29}=+0.252765261\) \(a_{30}=-0.149771953\)
\(a_{31}=+0.790218570\) \(a_{32}=-0.176776695\) \(a_{33}=-0.227703548\) \(a_{34}=-0.127782676\) \(a_{35}=+0.668150814\)
\(a_{36}=-0.387841811\) \(a_{37}=+0.947263251\) \(a_{38}=+0.263594642\) \(a_{39}=-0.770843573\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.264799789\) \(a_{42}=-0.500351261\) \(a_{43}=+1.193038082\) \(a_{44}=-0.240386077\) \(a_{45}=-0.346896262\)
\(a_{46}=+0.531921692\) \(a_{47}=-0.282017987\) \(a_{48}=+0.118405125\) \(a_{49}=+1.232127554\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.085588905\) \(a_{52}=-0.813777669\) \(a_{53}=+1.930600637\) \(a_{54}=+0.594676920\) \(a_{55}=-0.215007844\)
\(a_{56}=-0.528219599\) \(a_{57}=-0.176555832\) \(a_{58}=-0.178732030\) \(a_{59}=-1.171635785\) \(a_{60}=+0.105904763\)
\(a_{61}=-0.993924388\) \(a_{62}=-0.558768909\) \(a_{63}=-1.158895098\) \(a_{64}=+0.125000000\) \(a_{65}=-0.727864875\)
\(a_{66}=+0.161010723\) \(a_{67}=+0.264565034\) \(a_{68}=+0.090355997\) \(a_{69}=-0.356281434\) \(a_{70}=-0.472453972\)
\(a_{71}=+0.768439299\) \(a_{72}=+0.274245575\) \(a_{73}=+0.270121811\) \(a_{74}=-0.669816269\) \(a_{75}=+0.094724100\)
\(a_{76}=-0.186389559\) \(a_{77}=-0.718288330\) \(a_{78}=+0.545068718\) \(a_{79}=+0.219494968\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.377368703\) \(a_{82}=-0.894348508\) \(a_{83}=+1.777131230\) \(a_{84}=+0.353801769\) \(a_{85}=+0.080816860\)
\(a_{86}=-0.843605318\) \(a_{87}=+0.119714810\) \(a_{88}=+0.169978625\) \(a_{89}=-1.697928375\) \(a_{90}=+0.245292699\)
\(a_{91}=-2.431617545\) \(a_{92}=-0.376125436\) \(a_{93}=+0.374263714\) \(a_{94}=+0.199416831\) \(a_{95}=-0.166711890\)
\(a_{96}=-0.083725067\) \(a_{97}=-0.772994837\) \(a_{98}=-0.871245749\) \(a_{99}=+0.372927086\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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