Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 30.8419511661 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.570999285\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.110864248\) \(a_{7}=+1.041040118\) \(a_{8}=-0.353553391\) \(a_{9}=+1.468038753\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.038463424\) \(a_{12}=-0.785499642\) \(a_{13}=-0.991488165\) \(a_{14}=-0.736126527\) \(a_{15}=+0.702572239\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.346470188\) \(a_{18}=-1.038060158\) \(a_{19}=-0.881462159\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.635473281\) \(a_{22}=+0.734304529\) \(a_{23}=+0.381007173\) \(a_{24}=+0.555432124\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.701088005\) \(a_{27}=-0.735288547\) \(a_{28}=+0.520520059\) \(a_{29}=-0.352912167\) \(a_{30}=-0.496793594\)
\(a_{31}=+1.011477640\) \(a_{32}=-0.176776695\) \(a_{33}=+1.631425297\) \(a_{34}=+0.952098200\) \(a_{35}=-0.465567294\)
\(a_{36}=+0.734019377\) \(a_{37}=-0.047837872\) \(a_{38}=+0.623287870\) \(a_{39}=+1.557627198\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.707187861\) \(a_{42}=+1.156454248\) \(a_{43}=+1.587566032\) \(a_{44}=-0.519231712\) \(a_{45}=-0.656526889\)
\(a_{46}=-0.269412756\) \(a_{47}=-1.561741198\) \(a_{48}=-0.392749821\) \(a_{49}=+0.083764527\) \(a_{50}=-0.141421356\)
\(a_{51}=+2.115303702\) \(a_{52}=-0.495744082\) \(a_{53}=-1.038144883\) \(a_{54}=+0.519927518\) \(a_{55}=+0.464414962\)
\(a_{56}=-0.368063263\) \(a_{57}=+1.384776421\) \(a_{58}=+0.249546587\) \(a_{59}=-0.282624495\) \(a_{60}=+0.351286119\)
\(a_{61}=+1.651007528\) \(a_{62}=-0.715222698\) \(a_{63}=+1.528287237\) \(a_{64}=+0.125000000\) \(a_{65}=+0.443406987\)
\(a_{66}=-1.153591891\) \(a_{67}=-0.121684340\) \(a_{68}=-0.673235094\) \(a_{69}=-0.598561996\) \(a_{70}=+0.329205791\)
\(a_{71}=-1.862738358\) \(a_{72}=-0.519030079\) \(a_{73}=-1.419561804\) \(a_{74}=+0.033826484\) \(a_{75}=-0.314199857\)
\(a_{76}=-0.440731079\) \(a_{77}=-1.081082086\) \(a_{78}=-1.101408754\) \(a_{79}=-0.810390537\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.312900972\) \(a_{82}=+1.207164113\) \(a_{83}=+1.030887096\) \(a_{84}=-0.817736641\) \(a_{85}=+0.602159774\)
\(a_{86}=-1.122578707\) \(a_{87}=+0.554424762\) \(a_{88}=+0.367152265\) \(a_{89}=-0.070253767\) \(a_{90}=+0.464234615\)
\(a_{91}=-1.032178956\) \(a_{92}=+0.190503586\) \(a_{93}=-1.589030650\) \(a_{94}=+1.104317791\) \(a_{95}=+0.394201861\)
\(a_{96}=+0.277716062\) \(a_{97}=-1.461424982\) \(a_{98}=-0.059230465\) \(a_{99}=-1.524504551\) \(a_{100}=+0.099975586\)

Showing 100 of 254 available coefficients

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