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: \( 6.01171674499 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.703815723\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.497672871\) \(a_{7}=-0.475201469\) \(a_{8}=-0.353553391\) \(a_{9}=-0.504643428\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.784174717\) \(a_{12}=+0.351907862\) \(a_{13}=-1.461180564\) \(a_{14}=+0.336018181\) \(a_{15}=-0.314755960\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.136169559\) \(a_{18}=+0.356836790\) \(a_{19}=-0.643496019\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.334454266\) \(a_{22}=+0.554495260\) \(a_{23}=-1.272332876\) \(a_{24}=-0.248836435\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.033210685\) \(a_{27}=-1.058991702\) \(a_{28}=-0.237600735\) \(a_{29}=+1.113671950\) \(a_{30}=+0.222566074\)
\(a_{31}=+1.490684209\) \(a_{32}=-0.176776695\) \(a_{33}=-0.551914496\) \(a_{34}=-0.803393200\) \(a_{35}=+0.212516558\)
\(a_{36}=-0.252321714\) \(a_{37}=-1.319026064\) \(a_{38}=+0.455020399\) \(a_{39}=-1.028401855\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.340568617\) \(a_{42}=+0.236494879\) \(a_{43}=+0.037800118\) \(a_{44}=-0.392087359\) \(a_{45}=+0.225683402\)
\(a_{46}=+0.899675205\) \(a_{47}=-0.119762492\) \(a_{48}=+0.175953931\) \(a_{49}=-0.774183564\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.799654000\) \(a_{52}=-0.730590282\) \(a_{53}=-0.400446722\) \(a_{54}=+0.748820214\) \(a_{55}=+0.350693595\)
\(a_{56}=+0.168009091\) \(a_{57}=-0.452902616\) \(a_{58}=-0.787484988\) \(a_{59}=+0.884184070\) \(a_{60}=-0.157377980\)
\(a_{61}=-1.392490530\) \(a_{62}=-1.054072913\) \(a_{63}=+0.239807298\) \(a_{64}=+0.125000000\) \(a_{65}=+0.653459814\)
\(a_{66}=+0.390262483\) \(a_{67}=+0.831415170\) \(a_{68}=+0.568084779\) \(a_{69}=-0.895487883\) \(a_{70}=-0.150271899\)
\(a_{71}=+1.552544100\) \(a_{72}=+0.178418395\) \(a_{73}=-1.101723000\) \(a_{74}=+0.932692274\) \(a_{75}=+0.140763145\)
\(a_{76}=-0.321748009\) \(a_{77}=+0.372640978\) \(a_{78}=+0.727189926\) \(a_{79}=-1.798084000\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.240691583\) \(a_{82}=-0.947925160\) \(a_{83}=-0.289820000\) \(a_{84}=-0.167227133\) \(a_{85}=-0.508110473\)
\(a_{86}=-0.026728720\) \(a_{87}=+0.783819829\) \(a_{88}=+0.277247630\) \(a_{89}=-0.029560000\) \(a_{90}=-0.159582264\)
\(a_{91}=+0.694355151\) \(a_{92}=-0.636166438\) \(a_{93}=+1.049166984\) \(a_{94}=+0.084684870\) \(a_{95}=+0.287780168\)
\(a_{96}=-0.124418218\) \(a_{97}=+0.214099884\) \(a_{98}=+0.547430448\) \(a_{99}=+0.395728617\) \(a_{100}=+0.099975586\)

Showing 100 of 126 available coefficients

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